Wind Energy, the Price of Carbon, and Carbon Emissions: Evidence from Ireland
Kevin F. Forbes
Department of Business and Economics
The Center for the Study of Energy and Environmental Stewardship
The Catholic University of America
Washington, DC USA
Forbes@CUA.edu
Marco Stampini1
Inter-American Development Bank
Washington, DC USA
Ernest M. Zampelli
Department of Business and Economics
The Center for the Study of Energy and Environmental Stewardship
The Catholic University of America
Washington, DC USA
30th USAEE/IAEE North American Conference
Oct 9-11 2011
Washington DC
1
This paper reflects the opinions of the authors and not those of the Inter-American Development Bank, its
Board of Directors, or the countries they represent.
Abstract
This paper examines the effect of wind energy and outcomes in the European carbon market
on the carbon levels emitted by the power grid in the Republic of Ireland over the period 27
March 2008 through 15 August 2010. Using half-hour data on actual wind energy production,
forecasted wind energy production, forecasted load, actual load, the price of natural gas
relative to price of coal, the price of carbon allowances, the ex ante system price of
electricity, and the actual levels of carbon emissions, a model is estimated that examines the
contribution of wind energy, both load and wind forecasting errors, fuel prices, and the
carbon price on carbon emissions. The results of the analysis are expected to be of interest to
anyone with an interest in energy and climate policy.
Keywords: Climate Change, Renewable Energy, Wind Energy, Wind Forecasting
JEL Codes: Q2, Q4, Q5
1. Introduction
Because of the environmental concerns associated with fossil fuels use, considerable support
exists for increasing the share of electricity generation attributable to wind. For example, on
April 12, 2011, CaliforniaGovernor Edmund G. Brown, Jr. signed legislative bill SBX1 2 which
requires that one-third of California’s electricity come from renewable sources by 2020. This
policy initiative is expected to increase the wind energy capacity available to the California
Independent System Operator (ISO) by almost 500 per cent by 2020 (Hawkins, 2008). The
European Union has established a goal of 20 percent renewable energy by 2020 with wind
energy serving as a key source of the increase. And in China, whose installed wind capacity is
fifth largest in the world, wind power is expected to contribute 10 percent to its total electricity
needs by 2020 (Chen, et al., 2009).
These proposed increases in wind energy are predicated implicitly on the belief that an
increase in wind energy is an effective mechanism to reduce carbon emissions. But is it?
According to wind energy advocates, the answer is a definite “yes” since thereare no direct
carbon emissions associated with the production of electricity from wind turbines while the
production of electricity using coal gives rise to approximately one ton of CO2 emissions per
MWh. Consistent with this view, Cullen (2008) has presented evidence that eachMWh of wind
power in ERCOT, the power grid serving the vast proportion of Texas, offsets approximately one
ton of CO2emissions. However, the finding is open to question in light of evidence that wind
energy largely displaces natural gas, a fuel with a carbon emissions factor that is substantially
less than one ton per MWh. Moreover, the study fails to address a potentially important point-the relative unpredictability of wind energy may actually contribute to an increase in carbon
emissions at conventional power plants. For example, to maintain the reliability of the power
system, an over-prediction of wind energy levels may induce the system operator to dispatch a
generating unit that is highly carbon intensive while an under-prediction of wind energy may
increase the carbon intensity of the conventional plants that are dispatched down to
accommodate the unexpected wind energy production.
While most environmental economists tend to favor policy initiatives that would place a
price on carbon, the California energy crisis of 2000/2001,the oil price spike of 2007/2008, and
the 2008/2009 financial crisis, have contributed to a reluctance to rely on market processes in
remedying energy market inefficiencies. Increasingly, many are of the view that while markets
may “work” in the abstract, they are frequently deficient in practice. For example, the European
carbon trading system has been sharply criticized. Indeed, a 2009 study conducted by the
Friends of the Earth organization in the United Kingdom has concluded that Europe’s carbon
trading system is ineffective in reducing carbon emissions.
2. The Irish Power Grid
This paper examines the effect of wind energy and outcomes in the European carbon market on
the carbon levels emitted by the power grid in the Republic of Ireland over the period 27 March
2008 through 15 August 2010. Wind energy accounted for approximately 9.3 percent of load
over this period. The data for the analysis were obtained largely from EirGrid
(http://www.eirgrid.com), the system operator the Republic of Ireland. Electricity data was also
obtained from SEMO (Single Electricity Market Operator), which is a joint venture of
EirGridand the SONI (System Operator for Northern Ireland). As of November 2007, the overall
coordination of electricity production and consumption on the island is conducted by SEMO
(http://www.sem-o.com/Pages/default.aspx ). Table 1 reports the 2009 electricity supply capacity
for the entire island by fuel type.
Table 1
2009 Electricity Supply Capacity in Ireland by Fuel Type in Gigawatts (GW)
Wind
Other Renewables
Coal/Oil
CCGT
OCGT
Interconnector
Pumped Storage
1.5
0.6
3.2
3.5
0.7
0.5
0.3
Source: Pöyry Energy
EirGrid is one of the few system operators that reports carbon emissions in real-time on
its web site. The reported emissions are based on the fuel mix and the heat rates of the
generating units. Figure 1 reports the emissions for the first full week of 2010. Carbon intensity
was approximately 538 grams/KWh over the period27 March 2008 through 15 August 2010. To
put this number in perspective, the carbon intensity of the overall power grid in the United States
was approximately 600grams/KWh in 2008, the last year for which data are available. The Irish
government has a goal of reducing carbon intensity to 100 grams per KWh. Increasing the share
of generation from renewables such as wind energy is viewed as an important component of this
strategy. Specifically, wind energy capacity is expected to increase to at least 7.9 GW by 2035
(Pöyry Energy, 2010, p 52).
Figure 1. Carbon Emissions from the Republic of Ireland’s Power Grid, January 3 – 9,
2010
2000
1800
1600
Metric Tons Per Hour
1400
1200
1000
800
600
400
200
0
Source: EirGrid
EirGrid and SEMO also report actual wind energy production, forecasted wind energy
production, actual load, and forecasted load for the Republic of Ireland. Using this data, the
forecast accuracy of wind energy can be compared with that of load. The RMSE of the wind
forecastsis 29.4 percent of the mean level of wind energy production which is over seven times
the RMSE of the load forecasts relative to the mean level of load (Figure 2). The large
differential in the RMSEs is consistent with the findings of Forbes, et al. (2011) who have
reported large differences in the RMSEs between wind and load for a number of control areas
including Western Denmark, Eastern Denmark, 50Hertz in Germany, the Amprion system in
Germany,Terna in Italy, National Grid in the United Kingdom, the Midwest ISO in the USA, and
ERCOT in the USA. It may be noted that the RMSE of 29.4 percent appears much larger than
the six percentwind forecasting error for Ireland that was reported by Lang (2006). But the
calculation by Lang is weighted by wind energy capacity which we believe to be inappropriate.
Unfortunately, a number of other researchers including Cali, et. al (2006), Krauss et. al. (2006),
Holttinenet. al. (2006),Kariniotakiset. al, (2006),and Porter and Rogers (2010, p. 5)have also
chosen to report only capacity weighted RMSEs.
Figure 2. The Root-Mean-Squared-Errors of the Wind and Load Forecasts in Republic of
Ireland’s, 27 March 2008- 15 August 2010
35%
RMSE as a Percent of the Mean
Level of Wind and Load, Respectively
30%
25%
20%
15%
10%
5%
0%
Wind
Load
Based on an analysis of 41,577 half-hour observations. The data were obtained from
EirGrid and SEMO. The forecast errors are calculated based on the one-hour ahead wind
forecasts and four day ahead load forecasts.
3. A Model of Carbon Emissions
The amount of CO2 emitted by a power grid is determined not just by actual system demand
(load) and actual wind energy production but also by how closely these match up with what the
system operator had expected demand and wind energy production to be, as unexpected changes
in load and/or wind energy may force the system operator to undertake actions that increase (or
decrease) CO2 emissions from its conventional generating units. Additionally, changes in
relative fuel prices (natural gas and coal) and changes in the price of carbon (if applicable) will
have an impact on the optimal mix of generating units chosen by the system operator and hence
on the level of CO2 emissions as well. Consequently, we model carbon emissions as a function
of forecasted load, positive and negative load forecast errors, forecasted wind energy
production,positive and negative wind energy forecast errors, the spot price of natural gas
relative to the market price of coal, and the price of carbon relative to the ex ante system
electricity price established by SEMO. We include binary variables to control for each hour of
the day and for each month of the year. In its most general algebraic form, the model is given
by:
ln CO2  f ( forecasted load , one hour ahead wind forecast , positive wind forecast error ,
negative wind forecast error , positive load forecast error ,
negative load forecast error , gas / coal price rati o, carbon/electric p rice ratio ,
hourh , monthm )
where:

lnCO2 is the natural logarithm of CO2 emissions measured in metric tons per hour;

forecasted load is the forecasted level of electricity demand in MW;

one hour ahead wind forecastis the one hour ahead forecasted level of wind energy;
(1)

positive wind forecast errorequals the absolute value of the difference between the
forecasted and actual levels of wind energy when the forecasted level of wind energy is
greater than the actual and zero otherwise;

negative wind forecast error equals the absolute value of the difference between the
forecasted and actual level of wind energy in period t when the forecasted level of wind
energy is less than the actual and zero otherwise;

positive load forecast errorequals the absolute value of the difference between the
forecasted and actual level of demand when the forecasted level of demand is greater than
actual and zero otherwise;

negative load forecast errorequals the absolute value of the difference between the
forecasted and actual level of demand when the forecasted level of demand is less than
actual. It is zero otherwise;

gas/coal price ratioequals the spot price of natural gas relative to the price of coal where
both prices are expressed in EUR per MMbtu;

carbon/electric price ratio equals the European carbon price relative to the half-hour ex
ante system price of electricity established by SEMO.

houris a vector of binary variables representing each hour of the day exclusive of hour
one. Hour 1 is reflected in the overall constant term;

monthis a vector of binary variables representing each month of the year exclusive of
month 1, January. January is reflected in the overall constant term.
Data for each variable is reported for every thirty-minute period from 27 March 2008 to 15
August 2010. The initial estimation of (1) was conducted using the multivariable fractional
polynomial (MFP) model, a useful technique when one suspects that some or all of the
relationships between the dependent variable and the explanatory variables are non-linear
(Royston and Altman, 2008), but there is little or no basis, theoretical or otherwise, on which to
select particular functional forms. The MFP approach begins by estimating a model that is
strictly linear in the explanatory variables. In subsequent iterations, the algorithm cycles through
a battery of nonlinear transformations of the explanatory variables (positive and negative powers,
natural logarithms, etc.) until itconverges to the combination of functional forms that best
predicts the dependent variable. In our case, the analysis provided support for including
nonlinear forms for three of the explanatory variables, exclusive of hour and month binary
variables. Specifically, the MFP model obtained is given by:
ln CO2   0  1 ln( forecasted load )   2 (one hour ahead wind forecast )
  3 ( positive wind forecast error )   4 (negative wind forecast error )
  5 ( positive load forecast error )   6 (negative load forecast error )
(2)
  7 ( gas / coal price rati o) 3.0   8(carbon/ele ctric pric e ratio ) 0.5
24
12
h2
m2
   h hourh    m monthm
The hypothesized signs for each of the model’s coefficientsand their rationales are presented in
Table 2.
Table 2
Hypothesized Signs for Model Parameters
Variable
Coefficient
Hypothesis
ln(forecasted load)
β1
>0
one hour ahead wind forecast
β2
<0
positive wind forecast error
β3
>0
negative wind forecast error
β4
<0
positive load forecast error
β5
<0
negative load forecast error
β6
>0
(gas/coal price ratio)3.0
β7
>0
(carbon price ratio)-0.5
β8
<0
Rationale
More electricity consumption
increases electricity
production from fossil fuels
More wind energy reduces
electricity production from
fossil fuels
Lower than expected wind
energy increases reliance on
electricity produced using
fossil fuels
Higher than expected wind
energy reduces reliance on
electricity produced using
fossil fuels
Lower than expected
electricity demand reduces
electricity production using
fossil fuels
Higher than expected
electricity demand increases
electricity production using
fossil fuels
Higher relative price for
natural gas makes electricity
production from natural gas
less economic
Higher relative carbon price
makes electricity production
from fuels with higher carbon
emissions (e.g.coal) less
economic
Equation 2 was re-estimated using least squares with standard errors robust to arbitrary forms of
heteroscedasticity and autocorrelation.2 The results are reported in Table 3. For convenience,
we do not report the estimated coefficients for the hour and month binary variables.
Table 3
Parameter Estimates for MFP Functional Form with Robust Standard Errors
Variable
Est. Coef Std. Error
ln(forecasted load)
one hour ahead wind forecast
positive wind forecast error
negative wind forecast error
positive load forecast error
negative load forecast error
1.479533
-0.00049
0.000497
-0.00053
-0.00059
0.000533
(gas/coal price ratio)3.0
0..5
(carbon price ratio)
constant
Z-Value
P-Value
0.021507
1.08E-05
3.84E-05
3.92E-05
2.21E-05
2.76E-05
68.79
-45.08
12.95
-13.63
-26.66
19.31
0.000
0.000
0.000
0.000
0.000
0.000
0.012392
0.000478
25.95
0.000
0.015422
-5.17502
0.005467
0.169579
2.82
-30.52
0.005
0.000
Inspection of Table 3 reveals that all parameter estimates are highly statistically
significant, with p-values well below 0.01, and all are consistent with the hypothesized signs in
Table 2. Reductions in CO2 emissions can be expected with reductions in forecasted load and
increases in expected wind power.
To assess quantitatively the impact of a one MWh reduction in load, first note that:
 ln CO2
CO2
forecasted load


 ln( forecasted load ) ( forecasted load )
CO2
This means that:
2
Augmented Dickey-Fuller tests were conducted for all variables. The null hypothesis of a unit root was rejected in
all cases. Results are available upon request.
CO2
 ln CO2
CO2


 ( forecasted load )  ln( forecasted load ) forecasted load
(3)
Evaluating (3) at the sample mean values for CO2 and forecasted load, and using the (rounded)
point estimate of β1from Table 3 yields:
CO2
828.5
 1.48 
 0.402
 ( forecasted load )
3050.3
This in turn must be divided by two since forecasted load in the sample is measured in MW per
half-hour period. Consequently, a reduction in forecasted load of one MWh can be expected to
reduce emissions by approximately 0.2 metric tons per hour. This, of course, presumesno
change in load forecasting errors. Specifically, eachMWh increase in positive (negative) load
forecasting errors will yield subsequent reductions (increases) in CO2 emissions of 0.24 (0.22)
metric tons per hour.3
In calculating the expected emissions impact of a one MWh increase in forecasted wind
power, we note first that:
CO2
 ln CO2

 CO2
 (one hour ahead wind forecast )  (one hour ahead wind forecast )
,
This implies that a one MWh increase in forecasted wind energy production can be expected to
reduce CO2 emissions byabout 0.20metric tons per hour, presuming no change in wind
forecasting errors.4 A MWh increase in positive (negative) wind forecasting errors will generate
3
The calculation proceeds as follows:
CO2
 ln CO2

 CO2
( positive load forecasting error ) ( positive load forecasting error )
 0.00059  828.5  0.48
evaluated at the sample mean value of CO2. Dividing by two yields the -0.24 reported above.
Again, division by two is required since the forecasted wind
data is in MW per half-hour period.
4
This is equal to (-0.00049×828.5)/2.
an accompanying increase (decrease) of about 0.21 (0.22) metric tons of CO2 per hour.
The
results in Table 3 are consistent with our hypothesis that an increase (decrease) in the price of
natural gas relative to coal will serve to increase (decrease) carbon emissions, ceteris paribus.
Additionally, they are supportive of the hypothesis that an increase in the carbon price relative to
the electricity price will reduce emissions of CO2. Quantitatively, our estimates suggest that a
one percent decline in the relative price of natural gas reduces carbon emissions by about 1.4
metric tons per hour while a one percent increase in the relative carbon price reduces emissions
by 0.11 metric tons per hour.5
3.1 ARCH Effects
Time series regression with high frequency data—hourly, daily, weekly—can often be
plagued by the problem of time-varying volatility, more commonly referred to as Autoregressive
Conditional Heteroscedasticity (ARCH). In such instances, the variance (or volatility) of the
random disturbance term in time period t depends on the magnitudes of the random disturbances
from past periods. Algebraically, this can be represented by:
ht   0  1et21   2 et22  ...   q et2q
(1)
or, in shorthand, an ARCH(q) model, where ht is the error variance in time t and et2 s is the
squared error in time t-s. To test for ARCH effects, the basic model is estimated, the residuals
retrieved, and the following equation is estimated using least squares:
eˆt2   0  1eˆt21   2 eˆt22  ...   q eˆt2q
where êt is the residual for time period t. Significance of any αj indicates the presence of ARCH
effects.
5
Please refer to Appendix A for the derivations upon which these calculations are based.
Since our model does employ high-frequency time-series data, we tested for ARCH
effects using the residuals from the MFP estimation including up to 24 lags. A number of the
lagged squared residuals were statistically significant, though the marginal impact of the first
period lag clearly dominated with a point estimate of approximately 0.90, twenty to thirty times
the magnitudes of the other estimated coefficients.
Given the presence of significant ARCH effects, the model was re-estimated, with the
same MFP functional form, using the Generalized ARCH (GARCH) procedure. GARCH is
generally used to account for long lagged effects with a relatively small number of parameters.
Specifically, rewrite (1) as:
ht   0  1et21  11et22  121et23  ...  1q11et2q
effectively imposing a geometric lag structure where  s  1s 1 1et2 s . Now add and subtract β1α0
and rearrange terms on the right hand side to yield:
ht  ( 0  1 0 )  1et21  1 ( 0  1et22  121et23  ...  1q11et2q )
(2)
The last term in parentheses is nothing more than ht-1 and hence (2) can be written as:
ht   0  1et21  1ht 1
This is the standard GARCH(1, 1) model with one lagged h term and one lagged squared error
term. Its popularity derives from the fact that it can capture similar effects as an ARCH(q)
model with only three parameters rather than (q + 1) parameters.
The GARCH(1, 1) estimates are shown in Table 4. A comparison with Table 3 reveals
virtually the same results except for more precise standard errors and higher Z-values as a
consequence of modeling directly the ARCH process. Point estimates are of similar magnitudes
and hence lead to the same quantitative assessments as already discussed in the previous
subsection. We note also that both the lagged squared error and the lagged error variance are
statistically significant in the estimated error variance function.
Table 4
GARCH(1, 1) Estimates--MFP Functional Form
Variable
Est. Coef
Std. Error
Z-Value
P-Value
ln(forecasted load)
one hour ahead wind forecast
positive wind forecast error
negative wind forecast error
positive load forecast error
negative load forecast error
1.414419
-0.00047
0.000476
-0.00056
-0.00056
0.000496
0.001709
1.62E-06
7.15E-06
6.77E-06
4.47E-06
6.28E-05
775.72
-293.25
65.15
-87.48
-126.04
120.45
0.000
0.000
0.000
0.000
0.000
0.000
(gas/coal price ratio)3.0
0.012141
7.14E-05
117.8
0.000
(carbon price ratio-0.5
Constant
GARCH(1, 1)
lagged squared error
lagged variance
Constant
0.015668
-4.65938
0.000922
0.023626
25.38
-197.22
0.000
0.000
0.894295
0.044384
0.001006
0.017338
0.00562
1.94E-05
51.58
7.9
52
0.000
0.000
0.000
Finally, as a robustness check, we estimated two other versions of the model employing
GARCH(1, 1). The first assumed a log-linear form (dependent variable in natural log with right
hand side variables in linear form) while the second assumed a double-log form (all variables in
natural log form, except for the “error” variables). The results, reported in Appendix B, are
consistent with those reported in the text. The one exception is that the marginal impact of an
increase in the relative price of carbon seems to be greater for the alternative functional forms.
4. Summary and Conclusions
This paper has examined the effect of wind energy on the carbon levels emitted by the power
grid in the Republic of Ireland over the period 27 March 2008 through 15 August 2010. Using
half-hour data on forecasted and actual wind energy production, forecasted and actual load, the
price of natural gas relative to price of coal, the price of carbon allowances relative to the ex ante
system price of electricity, and the actual levels of carbon emissions, we estimated a model that
examined the contribution of wind energy, both load and wind forecasting errors, fuel prices, and
the carbon price on carbon emissions.
Based on the sample averages, the results suggest that a one MWh decrease in load and a
one MWh increase in wind power will reduce carbon emissions by almost the same amount, as
long as there are no offsetting changes in load and or wind forecasting errors. It is instructive to
note that our estimate of this reduction is far lower than that reported by Cullen (2008). As noted
in the introduction, Cullen’s analysis suggests that a one MWh increase in wind power reduces
emissions by one metric ton. The estimates presented in this paper suggest something much
smaller, on the order of only 0.2 metric tons. Moreover, based on the MFP suggested functional
form (where forecasted load is represented in the estimating equation in terms of its natural
logarithm while forecasted wind is modeled in terms of its actual level), there are diminishing
marginal returns to increases in wind energy production on carbon emissions. Accordingly,
increases in wind energy penetration above the current level may have only a minor impact on
the level of carbon emissions.
In contrast, our results seem to suggest that fairly small decreases in the price of natural
gas relative to coal and fairly small increases in the relative price of carbon can be very effective
in reducing emissions of CO2. This of course implies that the imposition of carbon taxes or the
establishment of well designed carbon cap-and-trade programs might be more cost-effective
ways of reducing carbon emissions than systems of wind power subsidies and tax credits.
Appendix A
To determine the change in CO2 emissions from a one percent change in the gas/coal price ratio,
we derive:
CO2
 ln CO2

 CO2  ( gas / coal price ratio)
 ln( gas / coal price ratio )  ( gas / coal price ratio)
 3  ˆ  ( gas / coal price ratio) 2  CO  ( gas / coal price ratio)
7
2
 3  0.012392  1.667  828.5  1.667
 142.34
2
using sample mean values. The value for this derivative suggests that a one percent increase
(decrease) in the gas/coal price ratio will cause a (142.34/100) or 1.4234 metric ton increase
(decrease) in CO2 emissions.
Similarly for the change in CO2 emissions from a one percent change in the
carbon/electricity price ratio, we derive:
CO2
 ln CO2

 CO2  (carbon price ratio)
 ln( carbon price ratio)  (carbon price ratio)
 0.5  ˆ8  (carbon price ratio) 1.5  CO2  (carbon price ratio)
 0.5  0.015422  0.332 1.5  828.5  0.332
 11.0822
Correspondingly, the value suggests that a one percent increase in the carbon/electricity price
ratio will cause a 0.11 metric ton decrease (increase) in CO2 emissions.
Appendix B
Table B1
GARCH(1, 1) Estimates--Log-Linear Functional Form
Variable
Est. Coef
Std. Error
Z-Value
P-Value
forecasted load
one hour ahead wind forecast
positive wind forecast error
negative wind forecast error
positive load forecast error
negative load forecast error
0.000442
-0.00044
0.000467
-0.00053
-0.00057
0.000501
1.09E-06
1.54E-06
6.52E-06
6.36E-06
3.20E-06
4.12E-06
404.61
-284.42
71.64
-83.01
-177.56
121.5
0.000
0.000
0.000
0.000
0.000
0.000
gas/coal price ratio
0.129848
0.000921
140.99
0.000
carbon price ratio
constant
GARCH(1, 1)
lagged squared error
lagged variance
constant
-0.12882
5.224772
0.003667
0.004884
-35.13
1069.81
0.000
0.000
0.895158
0.048036
0.048036
0.017438
0.005784
0.005784
51.33
8.31
8.31
0.000
0.000
0.000
Table B2
GARCH(1, 1) Estimates--Double Log Functional Form
Variable
Est. Coef
Std. Error Z-Value
P-Value
ln(forecasted load)
ln(one hour ahead wind forecast)
positive wind forecast error
negative wind forecast error
positive load forecast error
negative load forecast error
1.39459
-0.0966
0.0005
-0.0006
-0.0005
0.00048
0.00336
0.00041
6.71E-06
6.68E-06
4.26E-06
4.01E-06
415.12
-234.99
74.55
-84.85
-126.23
119.48
0.000
0.000
0.000
0.000
0.000
0.000
ln(gas/coal price ratio)
0.22154
0.00158
140.04
0.000
ln(carbon price ratio)
constant
GARCH(1, 1)
lagged squared error
lagged variance
constant
-0.0351
-4.1514
0.00107
0.0266
-32.73
-156.04
0.000
0.000
0.91009
0.04152
0.001
0.01757
0.00565
2E-05
51.8
7.35
48.98
0.000
0.000
0.000
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